While there were no aircraft attacks on Aruba during the war, there was noteworthy German submarine activity in the area due to Aruba being a vital oil producer for the Allied powers. Most notably on February 16, 1942, when a combined U-boat and Italian submarine wolfpack under the command of Werner Hartenstein in U-156 attacked the oil tankers and refineries at San Nicholas Harbor, Eagle Beach, and Willemstad Harbor, sinking six tankers and damaging a further two. One source I found noted that some Arubans turned on their lights and drove to the coast, to try and see what was going on.

In nighttime actions at sea, any light sorces are something that can be used to the attacker's advantage. A submarine could spot and attack a ship much easier and more successfully if the ship was sillouetted against a brightly lit-up island, for instance. There's also the danger of shore bombardment from the sub's deck guns, which could be much more accurately fired at a light source. U-156 herself was going to shell the Lago Refinery, which was a perfectly lit target, but fortunately her crew forgot to remove the plug from her 105mm deck gun, and the first shot rendered the gun inoperable for the time being. It was attempted to use the 37mm AA gun, but that proved ineffective.

This attack exposed how vulnerable Aruba was and how important it was that their crucial oil infrastructure remained functional, and afterwards, the island was ordered to completely black out for the remainder of the war. Why your grandparents thought that was a precaution against aircraft, I can't say. Maybe that was one of the justifications given thanks to either propaganda or just the fog of war, maybe it was rumor or gossip that spread, maybe they just misremembered it. But yes, Aruba did observe nighttime blackout protocols during WWII.